Analytical Approach of Unsteady Boundary-Layer Flows Over a Semi-Infinite Plate for All Strouhal Numbers

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Mohamed Bachiri ◽  
Ahcene Bouabdallah
Keyword(s):  
Boundary Layer ◽  
Strouhal Number ◽  
Boundary Layer Flow ◽  
Ad Hoc ◽  
Infinite Plate ◽  
Unsteady Boundary Layer ◽  
Boundary Layer Flows ◽  
Local Skin ◽  
Analytic Expressions ◽  
Layer Flow

In this paper, the unsteady boundary-layer flow over a semi-infinite flat plate is solved by means of an analytic approach. Via an ad hoc technique based on the boundary-layer flow evolution, an analytic expression of the velocity profile is proposed. The proposed formula verifies well the results given by Rayleigh, Blasius, and Williams–Rhyne for all time, thus for all Strouhal number values, which is the characteristic of the studied problem. As the main results, the local skin friction depending on a Strouhal number is given in an aim to show an explanation on the flow evolutions from the initial solution to the steady solution in the whole spatial region. This approach permits us to take many applications in engineering technology when the analytic expressions of the velocity, temperature, and matter are looked for.

scholarly journals On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
S. S. Motsa
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Boundary Layer Flow ◽  
Analysis Method ◽  
Unsteady Boundary Layer ◽  
Local Skin ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Spectral Homotopy Analysis Method

This work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non-linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms of bivariate Lagrange interpolation polynomials. The applicability and effectiveness of the expanded SHAM approach are tested on a non-linear PDE that models the problem of unsteady boundary layer flow caused by an impulsively stretching plate. Numerical simulations are conducted to generate results for the important flow properties such as the local skin friction. The accuracy of the present results is validated against existing results from the literature and against results generated using the Keller-box method. The preliminary results from the proposed study indicate that the present method is more accurate and computationally efficient than more traditional methods used for solving PDEs that describe nonsimilar boundary layer flow.

NATURAL CONVECTION BOUNDARY LAYER FLOW ALONG A SPHERE EMBEDDED IN A POROUS MEDIUM FILLED WITH A NANOFLUID

2014 ◽  
Vol 44 (2) ◽  
pp. 149-157
Author(s):  
A. M. RASHAD
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Extended Model ◽  
Local Skin ◽  
Layer Flow

 A boundary-layer analysis is presented for the natural convec tion boundary layer flow about a sphere embedded in a porous medium filled with a nanofluid using Brinkman-ForchheimerDarcy extended model. The model used for the nanofluid incorporates the ef fects of Brownian motion and thermophoresis. The governing partial differential equa tions are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature, and nanoparticles volume fraction profiles as well as the local skin-friction coefficient, local Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.

scholarly journals Numerical Solutions of Unsteady Boundary Layer Flow with a Time-Space Fractional Constitutive Relationship

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1446
Author(s):  
Weidong Yang ◽  
Xuehui Chen ◽  
Yuan Meng ◽  
Xinru Zhang ◽  
Shiyun Mi
Keyword(s):  
Boundary Layer ◽  
Numerical Method ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Constitutive Relationship ◽  
Elastic Behavior ◽  
Unsteady Boundary Layer ◽  
Time Space ◽  
Layer Flow ◽  
Fractional Parameter

In this paper, we develop a new time-space fractional constitution relation to study the unsteady boundary layer flow over a stretching sheet. For the convenience of calculation, the boundary layer flow is simulated as a symmetrical rectangular area. The implicit difference method combined with an L1-algorithm and shift Grünwald scheme is used to obtain the numerical solutions of the fractional governing equation. The validity and solvability of the present numerical method are analyzed systematically. The numerical results show that the thickness of the velocity boundary layer increases with an increase in the space fractional parameter γ. For a different stress fractional parameter α, the viscoelastic fluid will exhibit viscous or elastic behavior, respectively. Furthermore, the numerical method in this study is validated and can be extended to other time-space fractional boundary layer models.

Radiation effect on natural convection boundary layer flow over a vertical wavy frustum of a cone

2009 ◽  
Vol 223 (7) ◽  
pp. 1605-1614 ◽  
Author(s):  
M M Molla ◽  
M A Hossain ◽  
R S R Gorla
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Boundary Layer Flow ◽  
Average Rate ◽  
Local Heat Transfer ◽  
Convection Boundary Layer ◽  
Local Skin ◽  
Wide Range ◽  
Layer Flow

The effect of thermal radiation on a steady two-dimensional natural convection laminar boundary layer flow of a viscous incompressible optically thick fluid over a vertical wavy frustum of a cone has been investigated. The boundary layer regime when the Grashof number Gr is large is considered. Using appropriate transformations, the basic governing equations are transformed into a dimensionless form and then solved numerically employing two efficient methods, namely: (a) implicit finite difference method together with Keller-box scheme and (b) direct numerical scheme. Numerical results are presented by streamline, isotherms, velocity and temperature distribution of the fluid, as well as the local shearing stress in terms of the local skin-friction coefficient, the local heat transfer rate in terms of local Nusselt number, and the average rate of heat transfer for a wide range of the radiation—conduction parameter or Planck number Rd and the surface heating parameter θw.

Sign in / Sign up

Export Citation Format

Share Document